mlsanityData to 14 Oct 2026

The Fisher-Rao geometry of CES distributions

arXiv 2310.01032 ↗First posted 2 Oct 2023stat.ML cs.LG stat.APcited by 5

Not on the map. Why?

Abstract (arXiv)

When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as the Fisher-Rao information geometry. Interestingly, this yields a point of view that allows for leveragingmany tools from differential geometry. After a brief introduction about these concepts, we will present some practical uses of these geometric tools in the framework of elliptical distributions. This second part of the exposition is divided into three main axes: Riemannian optimization for covariance matrix estimation, Intrinsic Cram'er-Rao bounds, and classification using Riemannian distances.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 20 of its 101 references that are in the map. First posted on arXiv 2 Oct 2023.

Builds on

20 of 101 references.

References · 20

  1. 2018An elementary introduction to information geometrycited by 76
  2. 2016Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifoldscited by 64
  3. 2021On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometrycited by 32
  4. 2014Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matricescited by 20
  5. 2014A Plug&Play P300 BCI Using Information Geometrycited by 14
  6. 2014Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithmscited by 12
  7. 2014Regularized M-estimators of scatter matrixcited by 11
  8. 2023A numerical approximation method for the Fisher-Rao distance between multivariate normal distributionscited by 11
  9. 2015Robust Estimation of Structured Covariance Matrix for Heavy-Tailed Elliptical Distributionscited by 9
  10. 2021HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noisecited by 8
  11. 2021Robust low-rank covariance matrix estimation with a general pattern of missing valuescited by 8
  12. 2022Learning Graphical Factor Models with Riemannian Optimizationcited by 8
8 more
  1. 2013Multivariate Generalized Gaussian Distribution: Convexity and Graphical Modelscited by 6
  2. 2022Riemannian optimization for non-centered mixture of scaled Gaussian distributionscited by 4
  3. 2013On the Fisher information matrix for multivariate elliptically contoured distributionscited by 3
  4. 2020Riemannian geometry for Compound Gaussian distributions: application to recursive change detectioncited by 3
  5. 2022Robust Geometric Metric Learningcited by 3
  6. 2016Geodesic Convexity and Regularized Scatter Estimatorscited by 2
  7. 2016Simultaneous penalized M-estimation of covariance matrices using geodesically convex optimizationcited by 2
  8. 2023Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributionscited by 1

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Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 3.

5 papers.

  1. 2025SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challengescited by 6
  2. 2023Intrinsic Bayesian Cram'er-Rao Bound with an Application to Covariance Matrix Estimationcited by 1
  3. 2024Elliptical Wishart distributions: information geometry, maximum likelihood estimator, performance analysis and statistical learningcited by 1
  4. 2025Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifoldscited by 1
  5. 2025Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learningcited by 1